Excess-3
variation to BCD-code where three (11) is added to a binary representation
Excess-3, 3-excess or 10-excess-3 binary code (often abbreviated as XS-3, 3XS or X3), shifted binary or Stibitz code (after George Stibitz, who built a relay-based adding machine in 1937) is a self-complementary binary-coded decimal (BCD) code and numeral system. It is a biased representation. Excess-3 code was used on some older computers as well as in cash registers and hand-held portable electronic calculators of the 1970s, among other uses.
Representation
Biased codes are a way to represent values with a balanced number of positive and negative numbers using a pre-specified number N as a biasing value. Biased codes (and Gray codes) are non-weighted codes. In excess-3 code, numbers are represented as decimal digits, and each digit is represented by four bits as the digit value plus 3 (the "excess" amount):
The smallest binary number represents the smallest value (0 − excess).
The greatest binary number represents the largest value (2N+1 − excess − 1).
To encode a number such as 127, one simply encodes each of the decimal digits as above, giving (0100, 0101, 1010).
Excess-3 arithmetic uses different algorithms than normal non-biased BCD or binary positional system numbers. After adding two excess-3 digits, the raw sum is excess-6.
“Excess-3” enters the record as variation to BCD-code where three (11) is added to a binary representation. Crown Archives preserves that source wording while asking what Excess-3, variation and BCD-code can confirm, complicate or overturn.
Why this record matters
“Excess-3” is worth following because a concise public description often conceals a longer documentary argument. Here, Excess-3, variation and BCD-code provides the most credible route into that argument.
Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated May 11, 2026. The linked authority identifier is Q1076814. None of the 0 selected statements returned an explicit reference. The first chronological checks are 1937 and 1010.
The absence of detail may reflect summary conventions rather than a lack of surviving documentation. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
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Three-step research path
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- Expand the search: follow Excess-3 primary sources, Excess-3 archive and Excess-3 research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
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This entry incorporates text from “Excess-3” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.